We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
MiS Preprint
1/2024
Unified multivariate trace estimation and quantum error mitigation
Jin-Min Liang, Qiao-Qiao Lv, Zhi-Xi Wang and Shao-Ming Fei
Abstract
Calculating the trace of the product of $m$ $n$-qubit density matrices (multivariate trace) is a crucial subroutine in quantum error mitigation and information measures estimation. We propose an unified multivariate trace estimation (UMT) which conceptually unifies the previous qubit-optimal and depth-optimal approaches with tunable quantum circuit depth and the number of qubits. The constructed circuits have $\lceil(m-1)/s\rceil$ or $n\lceil(m-1)/s\rceil$ depth corresponding to $(s+m)n$ or $s+mn$ qubits for $s\in\{1,\cdots,\lfloor m/2\rfloor\}$, respectively. Such flexible circuit structures enable people to choose suitable circuits according different hardware devices. We apply UMT to virtual distillation for achieving exponential error suppression and design a family of concrete circuits to calculate the trace of the product of $8$ and $9$ $n$-qubit density matrices. Numerical example shows that the additional circuits still mitigate the noise expectation value under the global depolarizing channel.
